You are to roll a fair die n = 119 times, each time observing the number of dots appearing on the topside of the die. The number of dots showing on the topside of toss i is a random variable represented by Xi, i = 1,2,, 119. %3D ... (a) Consider the distribution of the random variable Xj. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll of this die. HX, = 3.500 Enter your answer using all the decimals you can. OX, = 1.708 Enter your answer using all the decimals you can. (b) Now think about the average of your n 119 tosses of the fair die. What can you say about the distribution of this average? Complete the sentence, Enter your answer using all the decimals you can. The distribution of X is skewed to the right A with a mean lx= 3.5 E and a standard deviation o 0.157 119 tosses will be (c) What is the probability that the average topside on your n = somewhere between 3.3 and 3.7? Enter your answer using all the decimals you can. (d) What is the probability that the average of your n= 119 tosses is greater than 4? Enter your answer using all the decimals you can.